MinT - Best Known (25, 104, s)-Nets in Base 32

Best Known (25, 104, s)-Nets in Base 32

(25, 104, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(25, 104, 177)-Net in Base 32 — Constructive

(25, 104, 177)-net in base 32, using

4 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(25, 104, 225)-Net over F₃₂ — Digital

Digital (25, 104, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 104, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(25, 104, 4670)-Net in Base 32 — Upper bound on s

There is no (25, 104, 4671)-net in base 32, because

1 times m-reduction [i] would yield (25, 103, 4671)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 108077 910462 403881 012610 730388 180396 584531 397174 382383 068788 507081 395689 643641 449460 425420 586160 728024 176025 985476 790810 870958 541004 803372 694590 316993 540888 > 32¹⁰³ [i]